From now on, we omit the markings from the notation, and study
deformations of a nodal marked curve \({\Sigma } = ({\Sigma },{z})\) . By \(T_{w_i^\pm } {\Sigma }\) , we mean the tangent space in
the component of \({\Sigma }\)  containing \(w_i^\pm \) . A gluing
parameter for the \(j\) -th node is an element \( \delta _i \in T_{w_i^+} {\Sigma } \otimes T_{w_i^-} {\Sigma } .\)  The canonical
conormal sequence [1]} gives rise to an exact sequence
\( 0 \rightarrow \operatorname{Def}_\Gamma ({\Sigma }) \rightarrow \operatorname{Def}({\Sigma }) \rightarrow \bigoplus _{i=1}^m T_{w_i^+} {\Sigma } \otimes T_{w_i^-} {\Sigma }\rightarrow 0 .\) 
